The core idea: pipelines, not CRS codes | Coordinate order and units | Inverse transformations | Matrix output | Validating pipelines | What's available

How a transformation is specified | Projections | Datum and reference-frame transforms | Geodetic computations | Adaptors, units and control | A note on the pipeline operator

The shared idea: an edge is a great circle | Where the work happens | Same shape, two readings | s2 can tessellate too | Using them together | Things that are the same, and things that are not | In one sentence

Origins: fasterize | The sparse insight | Integrating exactextract | Replacing GEOS: the native core | Unified geometry rasterization | Two burn modes | Coverage mode (default) | Approx mode | Performance | Current dependency tree | The three surfaces | Acknowledgements

Ear cutting | A real coverage | Constrained Delaunay: the PSLG route | Back to a triangle pool | The islands | Which engine | Further reading

What is a segment? | The cost of sealed geometry | What becomes easy | The full topology | Cycles and winding | The round trip | Integration: triangulation | Segments in movement data | Why this matters now | The lineage | Further reading

Why topology? | Basic workflow | Establish topology | Inspect the raw state | Access the pool components | Merge coincident vertices | Adjacency discovery | Shared edges | Internal boundaries | Neighbour graph | Ring and cycle analysis | Find closed cycles | Classify by winding | Arc-node topology | Round-trip to WKT | Periodic x (antimeridian) | Triangulation | Subsetting and combining | Building a pool from tables | Visualization | Related Work | Core topology/vertex-pool (hypertidy ecosystem) | Mesh/triangulation | Adjacency (computed, not stored)

The contract tables | Depth: inside, holes, and coverage | One-shot triangulation | The persistent handle | Refinement: angle, area, and sizing fields | Attributes ride along | Where to next

The example store | 1. Opening a store reads nothing | 2. One value reads one chunk | 3. The cache: reading it again is free | 4. Points: x[cbind(i, j, k)] is one planned request | 5. A rectangle: x[i, j, k] reads element by element | 6. The same rectangle, planned | 7. Materialization: when R wants all the data | 8. With a lower limit, materializing is refused | 9. Copies stay lazy until changed | 10. Saving stores the recipe, not the data | Where to go next

1. The smallest fetch function | 2. Test against a reference | 3. What altarr checks for you | 4. One call, many chunks | 5. Dimension order: reverse, never transpose | 6. Types, missing values and unpacking | 7. Recipes: what saveRDS() keeps | 8. Sources must be pinned | 9. Sketches for real backends | 10. Tools while developing

The same points, in two coordinate systems | GDAL does this too | Two GDAL defaults to know about | Where gdal_grid lives | Thin plate splines, in the other direction | A note on coordinate magnitude

Setup | Binning | What happens when two points land in one cell | Thin plate splines | Bilinear triangulation | Nearest neighbour | Inverse distance weighting | Kriging | Generalized additive models | Kernel smoothing | Akima (via the interp package) | What the pictures have in common | Where to next

The two tessellations | Barycentric coordinates | Two engines, one answer | The long way round, and a bug it revealed | The same thing, from a mesh | And back the other way

Where the cells are | Making one | Handing it to something else | What is not here

Step 1: find your collection | Step 2: is it actually alive, and what does it cover? | Step 3: run the audit | Step 4: look at it | When your collection doesn't play by MUR's rules | If your collection is cloud-hosted | Cheat sheet

Summary | The landscape: collections, granules, and this package's tools | Where it started: auditing one collection | Generalizing: finding out what's out there | Not every collection has granules | The S3 region gotcha | A silent correctness bug hiding in plain sight | Is this collection still alive? The ends_at_present rabbit hole | A quick-start for a new user

One collection, right now | ends_at_present, provider by provider, today | A small live liveness sample

The shared question | The scanline algorithm | Two answers to the boundary question | Cell-centre rule (fasterize / approx mode) | Exact coverage fractions (exactextract / coverage mode) | The same polygon, two classifications | Three motivational frames | fasterize: "which value goes in this pixel?" | exactextract: "what's the weighted aggregate under this polygon?" | controlledburn: "give me the geometry–grid relationship" | controlledburn's two code paths | Approx mode: the lightweight sweep | Coverage mode: the exactextract walker | From dense to sparse | Worked example: zonal statistics from sparse output | Summary

Seeing the layout | What image() does instead | From pixel stream to matrix and back | Multi-band arrays | Extent: cells have edges | Summary

Two functions, and the gap between them | ximage is a start on the finish | Index space: the default extent | Data that already knows its shape | Data that doesn't: the dimension guess | nativeRaster | Neighbours: png, nara, farver

Overview | SQLITE dialect (default) | Spatial SQL functions | GDAL-native functions (no SpatiaLite needed) | SpatiaLite functions (need SpatiaLite-enabled GDAL) | OGRSQL dialect | Direct SQL | GDAL quirks | Arrow stream interface | Geometry formats | Global options

Design | Conventions | Large grids | Compiled code | Headers | R reference implementations

Detailed Usage | Benchmarks of geodesic accuracy | Performance comparison

Examples | A polar example | Create the graticule as polygons | Comparison to tools in sp and rgdal | Notes | Terminology | References | Environment

Finding services | Discovering layers | Inspecting layers before downloading | Reading features | Multiple layers, same area | Spatial operations with geos | Working with different service types

Overview | The catalog | Chunking strategies | URL formats | *_gdal — zero configuration (recommended) | *_gdals3 — S3 protocol | *_s3 — S3 URI | *_url — raw HTTPS | Typical workflow | Refreshing the catalog | Why this works

Contents | Example Locations | MGRS - Military Grid Reference System | Basic Conversion | Understanding MGRS Codes | Precision Levels | Polar Regions (UPS) | Vectorized Operations | Geohash | The Truncation Property | Resolution by Length | Finding Required Length for Precision | Southern Hemisphere Examples | GARS - Global Area Reference System | GARS for Antarctic Locations | Georef - World Geographic Reference System | Georef for Flight Planning | Comparison of Systems | GeoCoords - Universal Coordinate Parsing | Parsing Various Formats | Parsing Multiple Coordinates | Integration with Other Functions | DMS - Degrees, Minutes, Seconds Conversion | Parsing DMS Strings | Parsing Coordinate Pairs | Parsing Angles and Azimuths | Encoding to DMS Strings | Output Formats | Splitting and Combining Components | Round-Trip Conversion | Integration with GeoCoords | See Also

Contents | Example Locations | The Inverse Problem: Distance and Bearing | Basic Distance Calculation | Understanding Azimuth | Distances Between Cities | Antarctic Distances | The Direct Problem: Finding Destinations | Basic Direct Calculation | Creating a "Circle" of Destinations | Antarctic Traverse Planning | Geodesic Paths | Sydney to London Great Circle | Antarctic Circle Path | Trans-Antarctic Path | Distance Matrices | City Distance Matrix | Antarctic Station Distances | Cross-Matrix: Cities to Antarctic Stations | Rhumb Lines (Loxodromes) | Geodesic vs Rhumb | East-West Travel | Rhumb Path | Polygon Area | Antarctic Ice Shelf Area | Multiple Polygons | Winding Direction Matters | Exact vs Fast Geodesic | Performance Comparison | Geodesic Intersections | Closest Intersection | Segment Intersection | Non-Intersecting Segments | Next Intersection | All Intersections Within a Distance | Practical Example: Great Circle Route Crossings | Vectorized Operations | Nearest Neighbor Search | Basic k-Nearest Neighbors | Multiple Query Points | Radius Search | Self-Search for Clustering | Distance Matrix | Performance | See Also

Contents | MGRS - Military Grid Reference System package provides R bindings to the | MGRS - Military Grid Reference System | UTM/UPS - Universal Transverse Mercator | Geohash | GARS - Global Area Reference System | Georef - World Geographic Reference System | Lambert Conformal Conic Projection | Azimuthal Equidistant Projection | Cassini-Soldner Projection | Gnomonic Projection | OSGB - Ordnance Survey National Grid | Local Cartesian (ENU) Coordinates | Geocentric (ECEF) Coordinates | WGS84 Ellipsoid | Geodesic Calculations | Inverse problem: distance and bearing between points | Direct problem: destination from start, bearing, and distance | Geodesic paths | Distance matrix | Rhumb Lines (Loxodromes) | Polygon Area | Polar Regions | Performance | Further Reading

Contents | Example Locations | Geocentric (ECEF) Coordinates | Basic Conversion | Understanding ECEF | Height Above Ellipsoid | Antarctic Stations in ECEF | Round-trip Conversion | GPS Applications | Local Cartesian (ENU) Coordinates | Local Survey Application | Including Height | Robotics/Navigation Application | WGS84 Ellipsoid Properties | Basic Parameters | Earth's Shape | Radii of Curvature | Circle of Latitude Properties | Auxiliary Latitudes | Combining Coordinate Systems | GNSS Data Processing | Antarctic Field Survey | Coordinate System Summary | See Also

Contents | Example Locations | UTM/UPS - Universal Transverse Mercator | Basic Conversion | Understanding UTM Zones | Polar Regions (UPS) | Round-trip Conversion | Transverse Mercator (Custom) | Lambert Conformal Conic (LCC) | Single Standard Parallel | Two Standard Parallels | LCC for Antarctica | Albers Equal Area | Two Standard Parallels (Most Common) | CONUS Albers (US Standard) | Antarctic Albers | Why Equal-Area Matters | Polar Stereographic | Antarctic Stations | Arctic Points | Pole at Origin | Azimuthal Equidistant | Distances from Sydney | Distances from South Pole | Cassini-Soldner Projection | Regional Mapping | Cassini for Antarctic Survey | Gnomonic Projection | Great Circle Routes Appear Straight | Route Planning | OSGB - Ordnance Survey National Grid | Grid References | Projection Comparison | See Also

Constrained triangulation of polygons | Example | Performance for developers | Orientation | Comparing paths and triangles | A geographic example | Variants | Performance

Raster data | OGRSQL | SQL Dialect | GDAL information

Installation | Usage | Performance | About

Example | Geometry collection is in development | Chaining together operations | Holes better work (or else)

What is PROJ? | Why PROJ? | What systems are supported? | How to use PROJ?

ALL | IJ | IA | FA

tabularaster | Examples | Simple examples | as tibble | Warnings | Applied example | Extract cell numbers | Extract cells from rasters

References

Topographic example

quadmesh | Why quadmesh? | Triangle mesh | Discrete forms | Quadmesh is a special case | Topology and geometry are completely separable | Geometry is purely a table of attributes | Point clouds are pure geometry | Polygons and lines in GIS are piecewise graphs

Implicit and explicit topology

silicate | MODELS | SC | PATH | ARC | TRI

R's matrix and array | Geographic raster | Internal storage of data in raster | Band order in raster native .grd format | ff can "map" these raw binary files